带股利分配的Black-Scholes市场中的最优投资-消费组合研究  

A Note on the Optimal Consumption and Portfolio in a Dividend-paying Fractional Black-scholes Market

作　　者：钟勇[1,2] 

机构地区：[1]武汉大学经济与管理学院博士后流动站 [2]中国长城资产管理公司博士后工作站

出　　处：《运筹与管理》2016年第4期168-171,共4页Operations Research and Management Science

摘　　要：针对经济个体有限财富的投资-消费分配问题,运用投资-消费组合期望效用最大化的评价方法,得出最优投资策略及预期收益。基于市场特性,以在带股利分配的、由多维分数次布朗运动驱动的Black-Scholes市场中的最优投资-消费问题为研究主题,并利用傅里叶分析工具,得到了对数和指数两种效用函数时的最优消费率和最优投资组合的显性表达式。Aiming at the investment-consumption distribution problems of the economic individual＇ s limited wealth, using the expected utility maximizing method of the investment-consumption portfolio, the optimal investment-consumption strategy and the expected return are obtained. In view of the market features, we focus on the problem in the dividend-paying Black-Scholes market driven by the multiple fractional Brownian motion; also with the aid of the Fourier analysis, the explicit expressions of the optimal consumption rate and the optimal portfolio in this market for an agent with utility functions of both power and logarithmic types are given.

关 键 词：分数次布朗运动 带股利分配的Black-Scholes市场 最优投资-消费组合 

分 类 号：F830.1[经济管理—金融学]